Extension to Reactions with Higher Orders

So far, only pseudo-first-order and instantaneous second-order reactions were discussed. In between there is the range of truly second-order behavior for which the continuity equations for A (Eq. 6.3.a-l) or B (Eq. 6.3.a-2), cannot be solved analytically, only numerically. To obtain an approximate analytical solution. Van Krevelen and Hoftijzer [3] dealt with this situation in a way analogous to that apfdied to pseudo-first-order kinetics, namely by assuming that the concentration of B remains approximately constant close to the interface. They mainly considered very fast reactions encountered in gas absorption so that they could set Cm - 0, that is, the reaction is completed in the film. Their development is in terms of the enhancement factor, F. The approximate equation for is entirely analogous with that obtained for a pseudo-first-order reaction Eq. 

This approximate solution is valid to within 10 percent of the numerical solution. Obviously when Cgi, C, then y = y and the enhancement factor equals that for pseudo-first-order. When this is not the case f is now obtained from an implicit equation. Van Krevelen and Hoftijzer solved Eq. 6.3.e-l and plotted F versus y in the diagram of Fig. 6.3.C-2, given in Sec. 6.3.c connecting the results for pseudo-first-order and instantaneous second-order reactions. 

Porter [7] and also Kishinevskii et al. [8] derived approximate equations for the enhancement factor that were found by Alper [9] to be in excellent agreement with the Van Krevelen and Hoftijzer equation (for Porter s equation when y 2) and which are explicit. Porter s equation is  

For an irreversible reaction of global order m + n(m with respect to A, n with respect to S), the approach followed by Hikita and Asai [10] was very similar to that of Van Krevelen and Hoftijzer. The rate of reaction was written as  

Furthermore, Cj was considered to be nearly constant in the film, while was again set zero. Hikita and Asai again cast the results into the form of a physical absorption rate multiplied by an enhancement factor 

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